How to Calculate Heat Flow in a Copper and Aluminum Rod Pairing?

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Homework Help Overview

The discussion revolves around calculating the rate of heat flow through a pairing of a copper rod and an aluminum rod in thermal equilibrium. The problem involves specific dimensions and thermal conductivities of the materials, as well as a temperature difference between the ends of the rods.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the heat flow equation and explore the relationship between the thermal resistances of the two materials. There are attempts to clarify the formula used for calculating heat flow, with some questioning the necessity of deriving everything from first principles.

Discussion Status

There is an ongoing exploration of the correct formula for heat flow, with some participants confirming the validity of the equations presented. However, there is no explicit consensus on the approach, as different interpretations of the formula are being discussed.

Contextual Notes

Participants note the importance of understanding the heat flow rate in both materials and question whether the length of the rods affects the calculations. There is also mention of the need for verification of the formulas used.

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Homework Statement



Hello, first question here,

A copper rod and an aluminium rod are in thermal equilibrium with each other. Copper rod = 50cm long and the aluminium rod is 20cm. Radius of pair is 8cm.
Copper end is heated (and maintained) at 80C , other end of pairing is 20C. k of copper is 390 and k aluminium is 210. Calculate the rate of heat flow through the pairing.

Homework Equations



Q/t = kA.(temperature difference, theta)/l

The Attempt at a Solution




Thanks for any help!
 
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That's not much of an attempt at a solution.
 
mgb_phys said:
That's not much of an attempt at a solution.

I think this is the answer, not 100%,

delta Q = delta T / SUM ( R )

=> DQ = DT / R1+R2...+...R0

R1 = 1 / k1A , R2 = 1 / k2A ,..., R0 = 1 / k0A
 
You should explain what you have done.
What do you know about the heat flow rate in both materials?
 
mgb_phys said:
You should explain what you have done.
What do you know about the heat flow rate in both materials?

I just need the equation, i am not going to derive everything from first principles, you can see what i have done,

Dt / sum of R where, R is as stated.

I am not William Thomson attempting to experimentally derive with this conclusion, i just have asked for a verification of the above formula.
 
Yes the formula is correct - it's pasted out of wikipedia.
The point of this site is to explain physics and help people understand it.
 
Thanks for your help!
 
Or should it be this,

= DQ = DT/ (L1/k1A + L2/k2A) where L = length of the rod. A = cross sectional area of rod.

i had,

DQ = DT / (1/k1A + 1/k2A)

Is it dependent on the length?
 

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